Final answer:
To find the mass of the volleyball, the impulse formula Impulse (I) = mass (m) * change in velocity (Δv) is used. With an impulse of -7.0 kg · m/s and a velocity change from 4.8 m/s to -23.6 m/s, the mass of the volleyball is calculated to be approximately 0.246 kilograms.
Step-by-step explanation:
The student's question involves finding the mass of a volleyball given the change in its velocity and the impulse applied. Impulse is defined as the change in momentum of an object and is calculated by the product of the force applied on the object and the time interval during which the force is applied. In formulaic terms, impulse (I) equals the change in momentum (Δp), which is also equal to the mass (m) times the change in velocity (Δv).
In this situation, the ball's velocity changes from 4.8 m/s to -23.6 m/s, and the impulse delivered is -7.0 kg · m/s. Therefore:
Impulse (I) = m * Δv = m * (final velocity - initial velocity)
-7.0 kg · m/s = m * (-23.6 m/s - 4.8 m/s)
-7.0 kg · m/s = m * (-28.4 m/s)
The mass m of the volleyball can be found by rearranging the equation:
m = -7.0 kg · m/s / (-28.4 m/s)
m = 0.246 kg
So the mass of the volleyball is approximately 0.246 kilograms.